**Author details**

**6. Conclusions**

**Figure 10.**

cross section.

waveguide.

**102**

This chapter presents two interesting types of dielectric materials in the straight rectangular waveguides and their applications. Five examples of the different discontinuous cross section were demonstrated. The effective technique was proposed for all case of **Figure 1a**–**e**, in order to calculate the dielectric material in the specific

*The output field as a response to a half-sine (TE*10*) input-wave profile for the hollow waveguide with four hollow rectangles, as shown in Figure 5b. The centers of the first, the second, the third and the firth hollow rectangles are located at the points (a/4, b/4), (3a/4, b/4), (a/4, 3b/4), and (3a/4, 3b/4), respectively. The parameters are a = b = 20 mm, c = d = 3.3 mm, and z = 15 cm, where hollow waveguide with four hollow*

*rectangles, as shown in Figure 1e, (a).* ϵ*<sup>r</sup> = 1.5; (b).* ϵ*<sup>r</sup> = 2; (c).* ϵ*<sup>r</sup> = 2.5; (d).* ϵ*<sup>r</sup> = 3.*

*Modern Applications of Electrostatics and Dielectrics*

The proposed techniques are very important to understand the influence of the dielectric materials and the hollow rectangles in all case of discontinuous geometry in the cross section. All the graphical results are demonstrated as a response to a halfsine (*TE*10) input-wave profile. The proposed techniques relate to the method based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. The method is based on Fourier transform, thus we need use with the image method to calculate the dielectric profile in the cross section. The image method and periodic replication are needed for fulfilling the boundary condition of the metallic

**Figure 8a**–**e** relates to the hollow rectangular waveguide where the hollow rectangle is located in the center of the cross section as shown in **Figure 4b**. We can find the relevant parameters to obtain the Gaussian behavior of the output field. From the results of **Figure 8a**–**e**, the Gaussian behavior is obtained when the thickness of the dielectric layer is equal to 3 mm. The output results are strongly

By increasing only the parameter ϵ*r*, the output dielectric profile increased, the output profile of the half-sine (*TE*10) profile decreased, and the output amplitude

affected by the thickness of the dielectric layer.

Zion Menachem Department of Electrical Engineering, Sami Shamoon College of Engineering, Beer Sheva, Israel

\*Address all correspondence to: zionme@sce.ac.il; zionmm@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
